Having mustered just one World Cup win in South Africa in 2010 and one point at the 2014 edition in Brazil, English fans were relieved to see their team scrape home 2-1 against Tunisia with an injury-time goal in their Group G opener on Monday.
"Now we can relax our way into the tournament and improve as time goes on," said 20-year-old Rashford, who came on as a substitute.
"There's no tension among the group or as individuals. But I think it's a new environment for a lot of us. Settling in can take a lot of time, but winning definitely speeds that transition up," Rashford added.
The speedy Manchester United forward lavishly praised "brilliant" captain and two-goal hero Harry Kane. He welcomed the use of Video Assistant Referee (VAR) technology even though England felt aggrieved it was not used to penalise manhandling in the box by the Tunisians.
"I'm sure it's something that will improve," Rashford said. "It's something that the game definitely needed."
With England due to face Panama on Sunday, Rashford said a quad injury suffered by Dele Alli was not looking too worrying. "I think he's going to get it all cleared up today ... Hopefully it's nothing too serious," he said.
"We've managed to get over the first hurdle, now we're going to analyse Panama and see how we can do ... I'm confident in the team to get three points."
Failures to win early World Cup games by big teams like Brazil and Germany have given England "a lot of confidence," he said, but a host of missed chances by the 'Three Lions' against Tunisia also showed improvement was needed.
"Obviously we want to be as clinical as we can be ... we definitely have to improve on that to win the tournament."
(Reporting by Andrew Cawthorne and Mike Holden, editing by Pritha Sarkar)
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